COLLIN COUNTY (CBSDFW.COM) – The number of people dying from the flu has gone up again in North Texas. Both Collin and Hunt County reported their first flu-related deaths of the season on Monday.

In all, 34 people in North Texans have died from flu-related complications so far this season – most of them in Dallas County.

A CBS 11 News crew saw the faces of the flu coming and going at a clinic in west Plano.

Medical professionals are saying there’s no shortage of vaccine, but you couldn’t tell that to a number of people who said they had problems getting their children protected.

It took a while but the Zapata family got what they wanted and were leaving a Plano clinic relieved. “We got the flu shots,” mother Veronica Zapata said excitedly. “CVS, Walgreens, I wasn’t wasn’t able to find it.”

A mission to get their seven-year-old daughter vaccinated against the flu took the Zapata’s to a Plano Wal-Mart and four pharmacies – each location turned them away.

The family was finally directed to an after hours clinic that they were told had only two doses left. Father Diego Zapata said, “It was very difficult. It’s not easy. We looked at many places.”

Over the weekend, as many as a 1,000 people waited in line for only 650 doses of the flu vaccine being offered for free to Plano residents. The city has now exhausted its supply and as the death toll rises, more people are wishing they had taken precautions.

The latest flu-related death is a Plano woman in her 50’s who authorities say did not get immunized and had other health problems.

For families like the Zapata’s, a flu shot offers peace of mind despite what may be a struggle to get it.